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Shrinking approximants for fixed point problem and generalized split null point problem in Hilbert spaces

Abstract

This paper deals with the convergence analysis of a shrinking approximants for the computation of a common solution associated with the fixed point problem of \(\eta \)-demimetric operator and the generalized split null point problem in Hilbert spaces. The considered sequence of approximants is a variant of the parallel hybrid shrinking projection algorithm that converges strongly to the optimal common solution under suitable set of control conditions. The viability of the approximants with parallel implementation is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature.

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Acknowledgements

The authors wish to thank the anonymous referees for their comments and suggestions. The authors (Y. Arfat, P. Kumam and P.S. Ngiamsunthorn) acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005. The author Yasir Arfat was supported by the Petchra Pra Jom Klao Ph.D Research Scholarship from King Mongkut’s University of Technology Thonburi, Thailand(Grant No.16/2562). Moreover, this project is funded by National Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract No. N41A640089).

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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to Poom Kumam or Muhammad Aqeel Ahmad Khan.

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Arfat, Y., Kumam, P., Khan, M.A.A. et al. Shrinking approximants for fixed point problem and generalized split null point problem in Hilbert spaces. Optim Lett (2021). https://doi.org/10.1007/s11590-021-01810-4

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Keywords

  • Shrinking approximants
  • Strong convergence
  • Fixed point problem
  • Demimetric operator
  • Generalized null point problem